Geodesic
Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 94-102.

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We study properties of symmetric stable measures with index $\alpha>2,\ \ \alpha\neq 2k,\ k\in\mathbb{N}$. Such measures are signed ones and hence they are not probability measures. We show that, in some sense, these signed measures are limit measures for sums of independent random variables.
Keywords: Large deviation problem, strictly stable random variable, limit theorems. 
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N. V. Smorodina; M. M. Faddeev. Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 94-102. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a11/

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[5] N. V. Smorodina, M. M. Faddeev, “The Lévy–Khinchin representation of a class of signed stable measures”, J. of Math. Sci., 159:3 (2009), 363–375